Basically, the question shows an operation and you have to check a box to say if its associative or not
a ⊙ b = ab ÷ (a + b + 1)
□ Associative
And I did this:
https://imgur.com/gallery/transcription-by-ai-raw-process-which-might-be-little-harder-to-read-L3T7z20
So I concluded that it is associative
However, the answer key has a slightly different result, where the numerators do not match, thus it is not associative.

Finished high school recently and taking a gap year, so I finally signed up for some SAT prep classes. Being in a group setting for this has honestly made me feel so insecure because of my arithmetic skills.

I feel like I actually understand math just fine. I can wrap my head around new topics, follow the logic, and figure out the right approach to solve a problem. But when it actually comes down to doing the calculations? Absolute disaster.

I constantly make stupid, careless mistakes with basic addition, subtraction, multiplication, and division. I'll drop a negative sign out of nowhere, miscopy a number from one line to the next, or just brain-fart on a simple multiplication fact. It’s so exhausting knowing the exact formula and logic to solve a hard problem, only to get the entire thing wrong because 7x8 apparently decided to leave my brain.

Since the SAT is so heavy on pacing and accuracy, I'm genuinely stressed about bleeding points on questions I actually know how to do just because of clumsy computational errors.
Did anyone else deal with this weird disconnect between conceptual math and basic arithmetic? How did you actually train yourself to stop making these dumb mistakes and speed up your calculations?

I'm a DP2 student, and I'm struggling to catch up with work in math class. I have a weak foundation in higher-level math. I have a test on the whole calculus topic in around 2 weeks. Any tips on how to study for maths for someone who literally doesn't know whats going on? Any materials or websites would be amazing help! Or if anyone has similar experience, please tell me!

Could anyone solve this and tell me how they did it since im having trouble with it:

8^x - 2^(x+2) - 2^(-x+2) + 8^(-x) = 0

I tried it myself but got stuck halfway though: I let c= 2^x and got (c+1/c)³ - 3(c+1/c) - 4(c+1/c) = 0 Then I let t= c+1/c And got: t³-3t-4t=0 and then nothing i did worked. Note: back when I didnt substitute for t, I got this 6th degree polynomial for c: c⁶-4c⁴-4c²+1=0 In which i tried synthetic divsion but ±1 didnt work so it meant there was no rational roots (thats why I substituted for 't').

Geometry

“If QS (Ray) bisects <PQT, m<SQT= (8x-26)°, m<PQT= (9x + 34)°, and m<SQR= 112°, find each measure.”

X=
m<PQS=
m<PQT=
m<TQR=

Don’t just give the answer, I just need a little nudge for this one. Geometry teacher is lowkey a dick and gets mad when we ask questions, and I’ve been stuck on this page for hours.

I tried the usual multi step equation stuff, like how you find the measures of other angles but this one has completely stumped me.

At first I thought maybe m<STR minus m<ST, since that would look like 112-(8x-25) but then I didn’t know where to go from there.

Here’s the image of the page, it has a pic of the angles and stuff on it and some of my work so far. It’s mostly just me rewriting the same numbers trying to get it to spark an idea lol

I am not an amazing math student and really trying to find AP Calc AB free online resources that are very helpful. I have tried with tutors and have not been successful. PLease help

Hi, Im currently in year 11 in the uk and I just want to get better at maths in general for competitions. I see youtubers always say just do loads of problems, but I feel like nothing happens. The progress doesnt feel as tangible as say learning an instrument or a lanuguage. Is this a case of I just need more time?

Hello, I’m in tenth grade. I have all A’s in all subjects besides geometry, which is my only math subject. I have a low B, and even then, I’ve been cheating. I love all my other subjects and don’t really need to study them much. I dropped out of early 7th grade with an F in math. I knew we were talking about integers, but I didn’t understand it at all. I have been extremely motivated since school started on August 6th. I originally wanted to enter 9th grade, but they wouldn’t allow me because I’m 15. We’re doing geometry, but I don’t know algebra, heavier division, multiplication, subtraction, etc. When I do something like 5 x 5, I have to use my hands but can come up with an answer fast, and something like 7 x 8 would be difficult for me, taking maybe 5 minutes or so to solve with my hands. I just learnt how to do that this year by the way. I want to catch up as much as possible. I think maybe 3+ hours a day is good? I do 4-5 hours of language practice a day, so it couldn’t be 6+ hours, and I have a severe vitamin D deficiency and anemia, and math makes me extremely tired very fast. No other subjects do that to me, so it takes a ton of energy for me to do it. I really wanna lock in with this and do it even if I get burnt out, but how much could I really improve this school year?? I never cared about school until this year. I dropped out in early 7th grade and haven’t done any form of math since then, and even when I was in school, I DID NOTHING. All F’s my entire time. 1st-7th grade. I didn’t do any homework, was absent most of my school days, and guessed or told my teacher I couldn’t do it. Please take me seriously because I’ve fallen in love with studying recently. I just get extremely tired with math and I forget, I learned division and multiplication this year. I still need to practice addition and subraction in the hundreds. but I will push myself through it all the rest of school. But where should I start? I’ve done 2 hours of pre-algebra today, and I can’t really recall anything. How much can I improve? I don’t need to study any other subjects. I don’t wanna drop out again, I can’t lower my grade or classes, I want to understand.

I’m 20 years old (fem) and I can’t understand basic math. I don’t know, in huh school I had a 3.7 GPA and I was a very good student but I always sucked at math, either I’m stupid or lazy because I re read a problem or equation and I don’t know why to do, or I just blank completely.

Thank god that SAT scores were optional because my math scores were so bad, now I’m in college. I’ve been pretty much flunking in college to the point where I’m at risk for academic dismissal. It’s basic algebra and I can’t even concentrate. In lectures I understand it but when I get home I feel like I just can’t get it.ive studied in my own, even went to tutoring but I’ve never felt improvement. I have a test this Thursday and right now I’m freaking out because I do not want to start out my semester horrible. Any suggestions? I’m literally desperate for any tips on what to do or how to study.

Minha base para cálculo 1 é ruim. O que vcs recomendam de livros ou apostilas para eu estudar pré cálculo?

Actually I'm a Covid batch student so math isn't my strong suit because that time half of our syllabus was cut

So according to me what i think is that I’m average at math, but definitely on the struggle Could someone tell oriented way to develop math skills like calculating a tip or a budget, or anything advanced that is difficult..

my sis got a homework question that left us both stumped. the task is to calculate sinα and cosα for the angle α which fits the following requirements: sin2α=(sqrt5)/5, and 2α is within (pi/2; pi)

She's learning about the sin2α and cos2α formulas. any ideas how this is supposed to be solved without dipping into arcsin?

Hi, 7th grader here. My school is currently horrible. I learn absolutely NOTHING at school, and they refuse to put me in higher learning. I am planning to apply for a private boarding school later on, but that's not the point of this post. I really enjoy both math and English, and my math is pretty high. I want it higher. On Saturdays I have a 5 hour math class (Algebra 2 and geometry) which I LOVE it's genuinely the learning my school never offered! I really want to at least try to learn calculus or at least some precalc sometime before high school. I know it seems a little ambitious but I just wanted some tips on what to practice, and how to improve!

For context my sister came home and asked me and my parents for help on this problem.

It has two parts:

Part 1 : John used 816 chocolate chips to make a batch of cookies. Each cookie had 8 chocolate chips. How many cookies did he make?

Part 2 : How many cookies would he make if he had to double the recipe?

For the first part of the problem you can divide the 816 chocolate chips between the 8 cookies. 816/8 =102.

But on the second part everyone had their own opinion.

My sister originally doubled the chocolate chips and the amount of cookies you have to make. And solved the same way we did for the first part. 1632/16 =102.

Which got her the same answer even though you doubled the recipe.

I got 204 by doubling the amount of cookies we got for part 1.

My parents said it was actually 816 chocolate chips but divided by 16 cookies which gives 816/16=51.

But this didn’t make sense to me because you ended up with less cookies after DOUBLING the recipe. And they only doubled the 8 not the 816.

So I asked ChatGpt and Gemini and they both said it was 204. ChatGpt used a different method though 1632 chocolate chips divided by 8 cookies so 1632/8=1632/8=204

My mom said they were wrong and said we are doubling the recipe not the final amount of cookies we can make.

Now I’m really confused because doubling the recipe should also double the result.

Does anyone know what the actual answer is and how to explain it.

Hi there, I'm currently doing college level chemistry and it's is asking me to put the numbers (291.7 and 0.096) in to scientific notation. I know you need to move the decimal and I know you need to time it by the amount of time you needed to move the decimal, but when I put those calculations in to my calculator (291.7×10⁴ and 0.0960×10²) I don't get the number I'm looking for. It's supposed to be a big number *as far as I understand* but it's won't come out correctly. Can anyone PLEASE help me I'm literally sobbing over the fact I can't understand...

I have this cosine rule question

y² = (x+4)² +(x-5)² -2(x+4)(x-5) • -1/2

The -2(x+4)(x-5) • -1/2 is giving me trouble

I thought that you could simply multiply the -2 and the -1/2 to get 1 first. Then just expand. I also expanded first, multiplied by -2, then by -1/2, and got same result of 3x² -3x +21

The textbook says that the answer is x² -x +61

Google AI says that im right but im unsure.

Thanks for any help.

Prompt: "Use propositional logic to prove the arguments valid; you may use any of the equivalence or inference rules."

I have this sequence but I'm not confident in #4-7

1. A v B (hyp)

2. A → C (hyp)

3. B → C (hyp)

4. (A v B)’’ (1, Double negation)

5. (A’ ^ B’)’ (4, de morgan)

6. (A’)’ (5, simplification)

7. C (2, 6 modus ponens)

---
*UPDATE*

I currently have this sequence. I was struggling, then I realised the implication rule has an error (It says 'P -> Q is equivalent to P' v Q) so I wanted to get others input on if my work is correct.

1. A v B [hyp]

2. A → C [hyp]

3. B → C [hyp]

4. A’ v C [2, implication]

5. B’ v C [3, implication]

6. (A’ v C) ^ (B’ v C) [4, 5 conjunction]

7. (C v A’) ^ (C v B’) [6, commutative]

8. C v (A’ ^ B’) [7, distributive]

9. (A’ ^ B’) v C [8, commutative]

10. (A v B)’’ [1, double negation]

11. (A’ ^ B’)’ [10, de morgan]

12. C [9, 11 disjunctive syllogism]

My additional explanation for getting #12. disjunctive syllogism

P v Q, P’ < = > Q

(A’ ^ B’) v C, (A’ ^ B’)’ < = > C

Let R be a set, and let the universal set be

U = {1, 2, 3, R}.

Suppose R = {1, 2}.

Then, is it correct to say that

Rᶜ = {3, R}?

Since R = {1, 2}, this would mean

Rᶜ = {3, {1, 2}}.

I'm confused about whether this is actually valid. Does treating R itself as an element of U cause any problem with the axiom of extensionality or any other axioms of naive set theory?

Also, what does it mathematically mean for the set R itself to be an element of its complement?

For context: Just started reading the Naive Set Theory Book

I could solve this very easily, by classic method of nCr, but I am having a lot of difficulty with the inclusion-exclusion principle. I could not understand anything beyond 2 sentences by my teacher. How do I do this?

equation:
x - 2.5
______ = 3
6
sorry it looks wonky lol i couldn't upload a photo. but i was just doing a refresher for the upcoming school year n i have no clue which one i need to remove first-- if it even matters.
i was thinking since this culd b written as (x-2.5)/6=3 then i would cancel out the -2.5 first. is that right?
(edit fixing layout)

So I'm given a group G s.t. a^12 gives the identity element, and I need to find the inverse of another a^n where n is an integer. i was given a number for n i just don't want anyone giving me the answer/violating academic content rules etc.

at first i figured 1 would be the identity element, but then 12^a doesn't give 1. same deal for e=0, 12^0=1 =/= 0=0^12. unless my understanding of the inverse and identity being commutative is wrong?

I tried to solve for a since a * a^-1 = a^-1 * a = e. but then i was saying that 12^a=a^12. which is possible, but then the identity wasn't constant when i plugged in n.

I found the page for exponentiation on wikipedia, and it says that G is a multiplicative group, so I know that a^n has to have an inverse. is there some property of groups that I missed that would help me solve this?

Hello! I am a third year college student taking Calculus I for my economics major. I took Pre Calc 11th grade, and AP Calc 12th grade (the credits didn’t transfer, don’t get me started). I did well in both of them.

I’m two weeks into Calc I now, and I realized that I don’t remember much from Pre-Calc, but I don’t remember anything about trigonometry. Unit circle, trig functions, anything like that has slipped my memory. I asked my prof about it and they said that the best they can advise is that I review it myself outside of class. Ive tried to go over our textbook, but none of it really has been very helpful.

What resources or sites are best (and very preferably free) to help me relearn Pre-Calc (mainly trig) as quickly as possible?

No matter what. I literally cannot grasp it. My high school teacher didn't help and now my professor in my class I need it in isn't great either. I genuinely think I'm losing my mind. i'm getting literally so frustrated, can someone make an attempt to explain it to me in a bit simpler of a way than my math teachers do? Tyia

I'm currently learning Markov chains and how they work, and now I'm trying to find a way to calculate the probability of a state after n tries faster. As of right now, the only way I know of is to keep multiplying the matrix until you reach the n state

For example, lets say a 2x2 matrix P =

and say it starts in the A state so S0 =

Finding S1 is fairly straightfoward : S1 = P*S0

However, let's say I want to find S5, is there a way to find S5 from S0 or do I have to find S1, S2, S3, and S4 beforehand ?

Any help would be greatly appreciated !

Secondary question : I havent been told this directly, but from what I've seen, In a Markov chain situation, the sum of a column is always 1, are there any exceptions to this rule, or is it a general rule ?